Monthly Archives: March, 2015

Emmy Noether (23 March 1882 – 14 April 1935) was born in the Bavarian town of Erlangen. Her father was the mathematician Max Noether and she studied Mathematics in the University of Erlangen where Max were teacher. She lectured her dissertation in 1907 under the supervision of Paul Gordan and after that she worked at the Mathematical Institute of Erlangen for seven years without any economical retribution! In 1915, David Hilbert invited her yo join him the Mathematics Department at the University of Gottingen. In that tiem, women were excluded from academic positions and she had to lecture her works under Hilbert’s name. Her habilitation was approved in 1919 and she became a leading member of the Department until 1933 when Germany’s Nazi government dismissed Jews from the university positions (she was Jewish!). She moved to USA where she lived until her death in 1935.

Source: Wikimedia Commons

Her contributions in abstract algebra were exposed by B. L. Van der Waerden in his influential 1931 textbook Moderne Algebra and her contributions were recognized around the world in the 1932 International Congress of Mathematicians in Zürich.

Another interesting museum located in the Collegius Maius of the Jagiellonian University is an exhibition about mathematics where children can play and learn a lot! There are old calculators from the 20th century…

Photography by Carlos Dorce

…abacus and slide rulers:

Photography by Carlos Dorce

Children can play with Geography and learn that straight lines in a map are not the shortest ways for the planes:

Photography by Carlos Dorce

They can also learn the theorem of Pythagoras scrolling this interesting figure:

Photography by Carlos Dorce

There are polyhedra and a lot of geometrical and topological games:

Photography by Carlos Dorce

The museum is very small but all the tourist are inside Collegius Maius so you can be very quiet watching all the exhibited objects and toys, like the Rodin’s Thinker:

Photography by Cristina Martínez

Finally… here you have my two children playing with Eulerian graphs! They are lovely! Aren’t they?

Copernicus studied in the Collegius maius between 1491 and 1495. On the list of 69 students matriculated in 1491 at the Cracok Academy were “Nicolaus Nicolai de Thuronia” and aslso his brother “Andreas Nicolai”. The Jagiellonian University consisted offour faculties at the time (the Theological Faculty, the Canonical La Faculty, the Medical Faculty and the Liberal Arts Faculty). Copernicus began his studies learning the grammar of Latin, poetry and rhetoric but he early started to attend lectures on Euclidean geometry and astronomy. During the 15th and early 16th centuries, the University gained importance in Central Europe as a scientific center due to the high level of astronomical and mathematical sciences: the distinguished professors of the time included Marcin Hrol (c.1422-c.1453), Wojciech of Brudzewo (1445-1495), Jan of Glogow (c.1445-1507) and Maciej of Miechow (1453-1523). In the second semester of 1493 he attended lectures of Jerzy Peürbach, with the comments of Wojciech of Brudzewo, and the lectures about Aristotle’s De Caelo. It’s unknown when Copernicus brothers finished their studies n Cracow but they surely didn’t receive their degrees. Perhaps their mother’s death in 1495 caused their return to Prussia.

Thus one of the required mathematical visits that must be done in Cracow is this College:

Photography by Carlos Dorce

The building hosts an interesting museum with a lot of old objects which are not directly related to the College but I must recognize that it’s possible to imagine how the academical life was in the 15th century. The first room is a big hall full of shelves with books, statutes, quadrants, portraits, maps and spheres:

Photography by Carlos Dorce

Everything takes you back to a ‘kitsch’ Renaissance:

Photography by Carlos Dorce

There is space for our Copernicus, of course,…:

Photography by Carlos Dorce

…and also for Galileo:

Photography by Carlos Dorce

There is a special small room dedicated exclusively to Copernicus with astrolabes, charts, books and copies of some interesting documents:

Photography by Carlos Dorce

For example, look at this interesting torquetum made by Hans Dorn in 1480 (the astrolabe was also made by Dorn in 1486)…:

Photography by Carlos Dorce

…or this portrait of Kepler from the 18th century:

Portrait of Johannes Kepler

Furthermore, a bust of Isaac Newton…

Photography by Carlos Dorce

… is on the top of the door through which you enter a room full of astronomical and mathematical instruments:

Photography by Carlos Dorce

Can you see this little Aechimedes screw?

Photography by Carlos Dorce

Before ending the visit, Newton (again!) says goodgye to the visitors in a very modern picture:

Photography by Carlos Dorce

And Kepler too!

Photography by Carlos Dorce

One thing more… Go to the ticket office and you will see some mathematical objects more like these English Napier Rods from the 17th century:

Gerardus Mercator was born in Rupelmonde (Belgium) exactly 503 years ago (and died in Duisburg on 2 December 1594). He was mathematician and cartographer and he is known for his word map of 1569 based on the projections which represented sailing courses of constant bearing as straight lines: